5 papers · 1 filter
Upper bounds for the ratio of the first two eigenvalues of the Robin Laplacian
Guowei Dai, Yingxin Sun
We sharpen upper bounds for the ratio of the first two Robin eigenvalues by matching the first eigenvalue on a comparison ball with an independently chosen boundary parameter. The…
Complete spectrum of the Robin eigenvalue problem on the ball
Guowei Dai, Yingxin Sun
We investigate the following Robin eigenvalue problem \begin{equation*} \left\{ \begin{array}{ll} -Δu=μu\,\, &\text{in}\,\, B,\\ \partial_\texttt{n} u+αu=0 &\text{on}\,\, \partial…
On the Schiffer and Berenstein conjectures with high-frequency for convex domains in the plane
Guowei Dai, Yingxin Sun, Juncheng Wei +1
In this paper, by introducing two-point stationary-phase amplitude defect, we provide a partial positive answer to the Schiffer and Berenstein conjectures in . More p…
Confirmed answer to the Schiffer conjecture and the Berenstein conjecture
Guowei Dai
Let be a bounded domain in with a connected () boundary. We show that, if the following overdetermined elliptic problem \begin{equation}…
Regularity and uniqueness to multi-phase problem with variable exponent
Guowei Dai, Francesca Vetro
In this paper, we consider a new class of multi phase operators with variable exponents, which reflects the inhomogeneous characteristics of hardness changes when multiple differen…